Time-dependent regimes of a Bursian diode II: Characteristic features of nonlinear oscillations

A study is made of the physical phenomena characteristic of nonlinear oscillations in a Bursian diode in the regime with a virtual cathode. The question of how the shape of the oscillations varies as the beam current density increases is investigated for the first time. Sharp jumps in the time evolution of the convective current are revealed, and their causes are explained. The reason is found for the onset of long-lived electrons, and their properties are analyzed.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

Microwave processes in the Octupole Galathea

Results are presented from experimental studies of electromagnetic emission and plasma oscillations in the plasma-frequency range in the Octupole Galathea confinement system. Experiments are performed in the electric-discharge mode at low magnetic fields (the barrier field is 0.002–0.01 T); the working gas is argon or hydrogen. It is found that the most intense microwave oscillations at frequencies of 1–5 GHz are excited near the plasma axis and in the magnetic-barrier region. The oscillations are excited by the discharge current and decay after the voltage is switched off. The experiments show that microwave oscillations excited in the magnetic-barrier region are responsible for the small value of the energy confinement time in the system.     

Causes and consequences of oscillations in the cerebellar cortex

Cerebellar high-frequency oscillations have been observed for many decades, but their underlying mechanisms have remained enigmatic. In this issue of Neuron, two papers indicate that specific intrinsic mechanisms in the cerebellar cortex contribute to the generation of these oscillations. Middleton et al. show that GABA(A) receptor activation and nonchemical transmission are required for nicotine-dependent oscillations at 30-80 Hz and 80-160 Hz, respectively, while de Solages et al. provide evidence that recurrent inhibition by Purkinje cells is essential for oscillations around 200 Hz.     

Representation of Time-Varying Stimuli by a Network Exhibiting Oscillations on a Faster Time Scale

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp.     

Mechanisms of firing patterns in fast-spiking cortical interneurons

Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na(+), delayed-rectifier K(+), and slowly inactivating d-type K(+) conductances. The model is analyzed using nonlinear dynamical system theory. For small Na(+) window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na(+) window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.     

A three-species model explaining cyclic dominance of Pacific salmon

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various—not fully convincing—explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as an attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.     

The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

Activation of passive iron as a model for the excitation of nerve

The activation by cathodic polarization of passive iron in concentrated nitric acid (d = 1.4) has been investigated. 1. For short current pulses (1 msec. or less) a transient activation occurs when the product of current density and time exceeds a certain value. This limiting value is here designated as the "threshold." It is of the order of magnitude of 200 x 10(-6) coulomb/cm.(2). 2. After activation and repassivation the threshold is temporarily several times higher than before. This "refractory state" is due to the presence of nitrous acid and of oxide layers. The return of the threshold to normal values occurs in seconds or minutes, depending on the variety of iron wire. 3. Immediately after a subthreshold current pulse the threshold is reduced (summation). However, if the second pulse occurs a certain interval of time after the first the wire exhibits a certain degree of refractoriness (Gildemeister effect). 4. Oscillographic measurements reveal the existence of a latent period between the application of the stimulating pulse and the establishment of the active state. The duration of this latent period depends on the strength of the current pulse. 5. There exists a minimum current density (rheobase) below which no activation occurs however long the current is applied. Depending on the variety of iron used this current density varies between about 1 and 10 ma./cm.(2). To produce activation a current of rheobasic strength does not have to be applied for an infinite time but only for about 100 msec. (maximum utilization time). Activation becomes manifest some time after termination of the activating pulse. 6. With currents of slowly increasing strength it is possible to reach current strengths several times higher than rheobase without obtaining activation (accomodation). Accomodation to a large extent depends on the variety of iron used. Details are given for currents increasing with a time constant of 0.5 second. 7. Potential measurements on wires in the refractory state show the existence of after potentials. Wires in the refractory state which are cathodically polarized show peculiar oscillograms. Both types of experiments point to the formation of nitrous acid as an essential element in the course of events. 8. With current densities only slightly above rheobase all wires exhibit simple activations only. With higher current densities certain types of wires exhibit periodic activations. The range of current densities in which such periodic activations occur varies with the type of wire. The lower limit is sometimes quite close to the rheobase. 9. A theory of periodic activations is presented which is modelled on the theory of self-excitatory electrical oscillations. As variables describing the state of the wire, the "degree of activation" and the "degree of refractoriness" are introduced. In the physicochemical system an autocatalytic process corresponds to the "falling characteristic" of electrical oscillations. The theory leads to a rational view of the interrelations between threshold, rheobase, accomodafion, refractoriness, and rhythm. The phenomena of conduction are not discussed here but their relation to the theory is briefly touched upon.     

Quantifying noise-induced stability of a cortical fast-spiking cell model with Kv3-channel-like current

Population oscillations in neural activity in the gamma (>30 Hz) and higher frequency ranges are found over wide areas of the mammalian cortex. Recently, in the somatosensory cortex, the details of neural connections formed by several types of GABAergic interneurons have become apparent, and they are believed to play a significant role in generating these oscillations through synaptic and gap-junctional interactions. However, little is known about the mechanism of how such oscillations are maintained stably by particular interneurons and by their local networks, in a noisy environment with abundant synaptic inputs. To obtain more insight into this, we studied a fast-spiking (FS)-cell model including Kv3-channel-like current, which is a distinctive feature of these cells, from the viewpoint of nonlinear dynamical systems. To examine the specific role of the Kv3-channel in determining oscillation properties, we analyzed basic properties of the FS-cell model, such as the bifurcation structure and phase resetting curves (PRCs). Furthermore, to quantitatively characterize the oscillation stability under noisy fluctuations mimicking small fast synaptic inputs, we applied a recently developed method from random dynamical system theory to estimate Lyapunov exponents, both for the original four-dimensional dynamics and for a reduced one-dimensional phase-equation on the circle. The results indicated that the presence of the Kv3-channel-like current helps to regulate the stability of noisy neural oscillations and a transient-period length to stochastic attractors.     

Investigation of low-frequency waves in plasma-filled microwave oscillators

The excitation of microwave oscillations by an electron beam in a hybrid plasma waveguide—a slow-wave structure (a sequence of inductively coupled resonators) with a plasma-filled transport channel—is studied both experimentally and theoretically. It is shown that the governing role in the generation of microwaves and their transmission to a feeder line is played by the spatial and temporal plasma-density variations associated with low-frequency ion plasma oscillations. The microwave pressure gives rise to low-frequency plasma oscillations with a rise time shorter than their period. This nonlinear mechanism for the excitation of low-frequency oscillations has a threshold in terms of the microwave power. The unsteady character of the spatial distribution of the plasma density results in intermittent microwave generation and shortens the duration of microwave pulses.     

The effects of refuges on predator-prey interactions: a reconsideration

Prey refuges are widely believed to prevent prey extinction and damp predator-prey oscillations. A review of the empirical evidence suggests that refuges are indeed capable of playing the former role. But the conditions under which they do so are not understood, nor is there any solid evidence for an effect on population fluctuations. The intuitive view that refuges act to stabilize equilibria and damp predator-prey oscillations is based in several theoretical studies of extremely simple models. Using a more realistic model, I show that several kinds of refuges can exert a locally destabilizing effect and create stable, large-amplitude oscillations which would damp out if no refuge was present. This finding contrasts sharply with the usual view. I argue that current evidence is tol weak, and the range of theoretically possible effects is too broad, to justify any simple characterization of refuge effects in nature. Manipulative empirical studies are an important first step toward correcting this situation, and I discuss some important factors to consider in their design.     

Spontaneous synchronous discharges in hippocampal slices. Simulation and experiment

Chaotic oscillations of extracellular potential of field-type nerve tissues are simulated by a 2D coupled map lattice. These tissues, say, the fields of the hippocampus, are represented by neural mass sheets consisting of current sources. The relationship between the source-sink ensembles and the extracellular field potential at each discrete instant of time t = 1, 2, ... is described by a single-site map creating chaos. The 2D coupled map lattice is viewed as a network of diffusively coupled the maps creating spatiotemporal chaos. The conversion of chaotic oscillations into synchronous ones, which are typical for epileptiform discharges, is studied. The results obtained are in good agreement with those derived from hippocampal slices treated with picrotoxin.     

Breaking of nonlinear cylindrical plasma oscillations

Nonlinear axisymmetric cylindrical plasma oscillations are investigated analytically and numerically. It is shown that the breaking of strongly nonlinear oscillations is attributed to a singularity in the electron density and occurs several periods after the onset of an off-axis density maximum. For weakly nonlinear conditions, an analytic dependence of the breaking time of the oscillations on their amplitude is obtained based on the effect of intersection of electron trajectories and is shown to agree with numerical results.     

Models of membrane resonance in pigeon semicircular canal type II hair cells

Pigeon vestibular semicircular canal type II hair cells often exhibit voltage oscillations following current steps that depolarize the cell membrane from its resting potential. Currents active around the resting membrane potential and most likely responsible for the observed resonant behavior are the Ca⁺⁺-insensitive, inactivating potassium conductance I _A (A-current) and delayed rectifier potassium conductance I _K. Several equivalent circuits are considered as representative of the hair cell membrane behavior, sufficient to explain and quantitatively fit the observed voltage oscillations. In addition to the membrane capacitance and frequency-independent parallel conductance, a third parallel element whose admittance function is of second order is necessary to describe and accurately predict all of the experimentally obtained current and voltage responses. Even though most voltage oscillations could be fitted by an equivalent circuit in which the second order admittance term is overdamped (i.e., represents a type of current with two time constants, one of activation and the other of inactivation), the sharpest quality resonance obtained with small current steps (around 20 pA) from the resting potential could be satisfactorily fit only by an underdamped term.     

TTX-Resistant NMDA Receptor-Mediated Membrane Potential Oscillations in Neonatal Mouse Hb9 Interneurons

Conditional neuronal membrane potential oscillations have been identified as a potential mechanism to help support or generate rhythmogenesis in neural circuits. A genetically identified population of ventromedial interneurons, called Hb9, in the mouse spinal cord has been shown to generate TTX-resistant membrane potential oscillations in the presence of NMDA, serotonin and dopamine, but these oscillatory properties are not well characterized. Hb9 interneurons are rhythmically active during fictive locomotor-like behavior. In this study, we report that exogenous N-Methyl-D-Aspartic acid (NMDA) application is sufficient to produce membrane potential oscillations in Hb9 interneurons. In contrast, exogenous serotonin and dopamine application, alone or in combination, are not sufficient. The properties of NMDA-induced oscillations vary among the Hb9 interneuron population; their frequency and amplitude increase with increasing NMDA concentration. NMDA does not modulate the T-type calcium current (I_Ca(T)), which is thought to be important in generating locomotor-like activity, in Hb9 neurons. These results suggest that NMDA receptor activation is sufficient for the generation of TTX-resistant NMDA-induced membrane potential oscillations in Hb9 interneurons.     

Oscillations in an Intra-host Model of <Emphasis Type="Italic">Plasmodium Falciparum</Emphasis> Malaria Due to Cross-reactive Immune Response

We consider an intra-host model of malaria that allows for antigenic variation within a single species. More specifically, the host’s immune response is compartmentalized into reactions to major and minor epitopes. We investigate the conditions that lead to transient oscillations, which correspond to recurrent clinical episodes of the diseases, and how a small delay in the activation of the immune response can lead to persistent oscillations. We find that the efficacies of the immune responses to the major and minor epitopes, defined in terms of rate constants, play a crucial role in determining when there will be transient oscillations. The delay necessary to excite persistent oscillations, the time duration between disease episodes and their severity are also expressed in terms of the immune response efficacies. In addition, we describe how the severity and duration of the oscillations depend upon the parasite propagation rates and the immune response efficacies.     

Ba2+ current oscillations modulated by cyclic AMP and phorbol esters in ras-transformed fibroblasts.

An oscillatory influx of divalent cations was measured as Ba2+ inward currents (Ba2+ current oscillations) by voltage-clamp recording in v-Ki-ras-transformed NIH/3T3 (DT) fibroblasts after activation with bradykinin or serum. Application of forskolin or dibutyryl cyclic AMP onto DT cells initiated Ba2+ current oscillations. Increasing intracellular cyclic AMP reduced the amplitude but increased the frequency of the Ba2+ current oscillations. Activation of protein kinase C by phorbol esters terminated Ba2+ current oscillations. No inhibition of Ba2+ current oscillations by phorbol esters was observed in down-regulated cells that had been pretreated with phorbol esters for 24 hrs. The results suggest that Ba2+ current oscillations are regulated by intracellular second messengers.